- Function Method for Repulsive Casimir Forces

Since Casimir's paper [1] on the attraction of two neutral parallel (perfectly) conducting plates due to the vacuum uctuations of the electromagnetic eld, a considerable amount of work has been done on this subject, varying from the application of alternative techniques to the exploration of new geometries and theories. Excellent reviews as well as a large list of relevant references on this subject can be found in the work of Plunien et al[2] and in the book by Mostepanenko and Trunov[3]. The rst experimental test of Casimir's prediction was made by Sparnaay[4] only in 1958. However, the accuracy of the results was far from being reasonable: approximately one hundred percent of error. Since then, experiments involving dielectrics have been done, but only four decades after Sparnaay's work an experiment of the Casimir force between metals was repeated: in 1997, Lamoreaux[5] made an experiment with a slightly di erent geometry (a spherical metallic lens and a at metal plate) where theory and the experimental data agree within a few percents. More recently, another experiment with metals was performed by U. Mohideen and A. Roy [6]. Using an atomic force microscope they measured the Casimir force between a metallized sphere of diameter equal to 196 m and a at metal plate for separations from 0; 1 m to 0; 9 m. They showed that the experimental data are in very good agreement with the theoretical predictions. May be this is one of the most striking results of quantum eld theory once it is a macroscopic (measurable) manifestation of the quantum vacuum.